Tunneling spectroscopy reveals evidence for interlayer electron-hole correlations in quantum Hall bilayer two-dimensional electron systems at layer separations near, but above, the transition to the incompressible exciton condensate at total Landau level filling ν_T=1. These correlations are manifested by a non-linear suppression of the Coulomb pseudogap which inhibits low energy interlayer tunneling in weakly-coupled bilayers. The pseudogap suppression is strongest at ν_T=1 and grows rapidly as the critical layer separation for exciton condensation is approached from above.

When two 2D electron gas layers, each at Landau level filling factor $\nu=1/2$, are close together a condensate of interlayer excitons emerges at low temperature. Although the excitonic phase is qualitatively well understood, the incoherent phase just above the critical layer separation is not. Using a combination of interlayer tunneling spectroscopy and conventional transport, we explore the incoherent phase in samples both near the phase boundary and further from it. In the more closely spaced bilayers we find the electronic spectral functions narrower and the Fermi energy of the $\nu = 1/2$ composite fermion metal smaller than in the more widely separated bilayers. We attribute these effects to a softening of the intralayer Coulomb interaction due to interlayer screening.

In a bilayer system consisting of a composite-fermion (CF) Fermi sea in each layer, the tunnel current is exponentially suppressed at zero bias, followed by a strong peak at a finite-bias voltage V-max. This behavior, which is qualitatively different from that observed for the electron Fermi sea, provides fundamental insight into the strongly correlated non-Fermi-liquid nature of the CF Fermi sea and, in particular, offers a window into the short-distance high-energy physics of this highly nontrivial state. We identify the exciton responsible for the peak current and provide a quantitative account of the value of V-max. The excitonic attraction is shown to be quantitatively significant, and its variation accounts for the increase of V-max with the application of an in-plane magnetic field. We also estimate the critical Zeeman energy where transition occurs from a fully spin-polarized composite-fermion Fermi sea to a partially spin-polarized one, carefully incorporating corrections due to finite width and Landau level mixing, and find it to be in satisfactory agreement with the Zeeman energy where a qualitative change has been observed for the onset bias voltage [J. P. Eisenstein et al., Phys. Rev. B 94, 125409 (2016)]. For fractional quantum Hall states, we predict a substantial discontinuous jump in V-max when the system undergoes a transition from a fully spin-polarized state to a spin singlet or a partially spin-polarized state.

Double layer two-dimensional electron systems at high perpendicular magnetic field are used to realize magnetic tunnel junctions in which the electrons at the Fermi level in the two layers have either parallel or antiparallel spin magnetizations. In the antiparallel case the tunnel junction, at low temperatures, behaves as a nearly ideal spin diode. At elevated temperatures the diode character degrades as long-wavelength spin waves are thermally excited. These tunnel junctions provide a demonstration that the spin polarization of the electrons in the N=1 Landau level at filling factors ν=5/2 and 7/2 is essentially complete, and, with the aid of an in-plane magnetic field component, that Landau level mixing at these filling factors is weak in the samples studied.

Electron tunneling spectroscopy measurements on van der Waals heterostructures consisting of metal and graphene (or graphite) electrodes separated by atomically thin hexagonal boron nitride tunnel barriers are reported. The tunneling conductance, dI/dV, at low voltages is relatively weak, with a strong enhancement reproducibly observed to occur at around |V| ≈ 50 mV. While the weak tunneling at low energies is attributed to the absence of substantial overlap, in momentum space, of the metal and graphene Fermi surfaces, the enhancement at higher energies signals the onset of inelastic processes in which phonons in the heterostructure provide the momentum necessary to link the Fermi surfaces. Pronounced peaks in the second derivative of the tunnel current, d2I/dV2, are observed at voltages where known phonon modes in the tunnel junction have a high density of states. In addition, features in the tunneling conductance attributed to single electron charging of nanometer-scale defects in the boron nitride are also observed in these devices. The small electronic density of states of graphene allows the charging spectra of these defect states to be electrostatically tuned, leading to "Coulomb diamonds" in the tunneling conductance.

The Coulomb gap observed in tunneling between parallel two-dimensional electron systems, each at half-filling of the lowest Landau level, is found to depend sensitively on the presence of an in-plane magnetic field. Especially at low electron density, the width of the Coulomb gap at first increases sharply with in-plane field, but then abruptly levels off. This behavior appears to coincide with the known transition from partial to complete spin polarization of the half-filled lowest Landau level. The tunneling gap therefore opens a window onto the spin configuration of two-dimensional electron systems at high magnetic field.

We report simultaneous quasi-dc magnetotransport and high-frequency surface acoustic wave measurements on bilayer two-dimensional electron systems in GaAs. Near strong integer quantized Hall states, a strong magnetic-field-sweep hysteresis in the velocity of the acoustic waves is observed at low temperatures. This hysteresis indicates the presence of a metastable state with anomalously high conductivity in the interior of the sample. This nonequilibrium state is not revealed by conventional low-frequency transport measurements which are dominated by dissipationless transport at the edge of the two-dimensional system. We find that a field-cooling technique allows the equilibrium charge configuration within the interior of the sample to be established. A simple model for this behavior is discussed.

Clean two-dimensional electron systems in GaAs/AlGaAs heterostructures exhibit anisotropic collective phases, the quantum Hall nematics, at high Landau level occupancy and low temperatures. An as yet unknown native symmetry-breaking potential consistently orients these phases relative to the crystalline axes of the host material. Here we report an extensive set of measurements examining the role of the structural symmetries of the heterostructure in determining the orientation of the nematics. In single quantum well samples we find that neither the local symmetry of the confinement potential nor the distance between the electron system and the sample surface dictates the orientation of the nematic. In remarkable contrast, for two-dimensional electrons confined at a single heterointerface between GaAs and AlGaAs, the nematic orientation depends on the depth of the two-dimensional electron system beneath the sample surface.

We investigate electron tunneling through atomically thin layers of hexagonal boron nitride (hBN). Metal (Cr/Au) and semimetal (graphite) counter-electrodes are employed. While the direct tunneling resistance increases nearly exponentially with barrier thickness as expected, the thicker junctions also exhibit clear signatures of Coulomb blockade, including strong suppression of the tunnel current around zero bias and step-like features in the current at larger biases. The voltage separation of these steps suggests that single-electron charging of nanometer-scale defects in the hBN barrier layer are responsible for these signatures. We find that annealing the metal-hBN-metal junctions removes these defects and the Coulomb blockade signatures in the tunneling current.

Most often, the electrical properties of a material are described as either "conducting" or "insulating". Copper, everyone knows, is a good conductor. It is the foundation of the electrical infrastructure of the nation. Glass, on the other hand, is an excellent insulator. But do these two words describe all the possibilities? The answer is emphatically no, and the basic subject of the research funded by this grant is aimed at fleshing out a more complete description of the electrical properties of materials. Many people are aware that there are also special materials called superconductors. A superconductor (e.g. aluminum when cooled to very low temperatures) is like a regular conductor except that it conducts electricity with no energy loss at all. Ordinary metals get hot when current flows through them; witness the toaster in your kitchen. In a superconductor something very special is going on: The electrons in the metal don't behave individually as they do in an ordinary conductor. Instead they act collectively. It is this collective aspect that makes superconductors so interesting to physicists. So now we have metals, insulators and superconductors. Is there anything else? We now know the answer is yes. In this research we examine special conducting materials, ones in which the mobile electrons are confined to move on a plane surface (as opposed to motion in all three directions). Examples of such "2D" materials include electrons confined to the interface between two otherwise insulating materials (as in the so-called "semiconductor heterostructures" used here) and the single atomic layer of carbon atoms now known as "graphene". Materials like these are not just museum curiosities; each of the billions of transistors in every smart-phone has a 2D electron system in it. In the work supported by this grant, the focus is on both collective conducting states in semiconductor heterostructures and on the conducting properties of graphene and its few-layer cousins. In particular, the exotic collective (and deeply quantum mechanical) electronic phases which develop when a large magnetic field is applied have been a major focus of effort. Significant results have been obtained from both ordinary electrical measurements and from more sophisticated thermoelectric studies of such systems. Related studies of few-layer graphenes have elucidated the transition from the two- to three-dimensional electrical properties of carbon-based conductors. Investigations like these expand our understanding of electronic materials general. While there are certainly immediate fundamental scientific pay-offs, it is also true that research of this kind ultimately leads to technological breakthroughs in the long term. By way of example, superconductivity was undoubtedly regarded as a useless novelty when it was discovered in 1911. Who could have known then that it would become crucial to the medical revolution brought about by magnetic resonance imaging decades later?

The electronic transport properties of single layer graphene having a dilute coating of indium adatoms has been investigated. Our studies establish that isolated indium atoms donate electrons to graphene and become a source of charged impurity scattering, affecting the conductivity as well as magnetotransport properties of the pristine graphene. Notably, a positive magnetoresistance is observed over a wide density range after In doping. The low field magnetoresistance carries signatures of quantum interference effects which are significantly altered by the adatoms.